1 F eb 1 99 9 A proof of a conjecture for the number of ramified coverings of the sphere by the torus ∗
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چکیده
A proof of a conjecture for the number of ramified coverings of the sphere by the torus * Abstract An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson and Vainshtein for the explicit number of such coverings.
منابع مشابه
A Proof of a Conjecture for the Number of Ramified Coverings of the Sphere by the Torus
Let X be a compact connected Riemann surface of genus g"0. A ramified covering of S of degree n by X is a non-constant meromorphic function f : X!S such that | f (q)|=n for all but a finite number of points q # S, which are called branch points. Two ramified coverings f1 and f2 of S by X are said to be equivalent if there is a homeomorphism ? : X!X such that f1= f2 b?. A ramified covering f is ...
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تاریخ انتشار 1998